The present invention pertains to demodulators, and more specifically, demodulators for shaped binary phase shift keyed (shaped BPSK) signals. Shaped BPSK modulation is similar to conventional BPSK modulation except, in shaped BPSK modulation, abrupt phase transitions are avoided and the spectrum occupies a smaller bandwidth. Shaped BPSK modulation is useful in radio equipment applications where only a narrow satellite channel is available for relaying the signal. Effective demodulation of shaped BPSK signals is made difficult since the portion of the signal caused by the linear phase transition of the shaped BPSK signal causes unwanted signal power in a Q channel of a demodulator. Conventional demodulators, such as Costas demodulators, are unable to eliminate, or at least minimize, this unwanted Q channel signal power and, therefore, such a demodulator fails to track shaped BPSK signals having a high data transition. Also, carrier lock detectors based upon comparisons of relative power levels of an I channel and a Q channel fail because of the unwanted Q channel signal power.